A model from a minimal sample, not from all the data
In June 1981 Martin Fischler and Robert Bolles published RANSAC. Rather than averaging every measurement, the method draws the smallest number of points a hypothesis needs, builds a model, and counts how much of the rest agrees with it. In an experiment on twenty landmarks of which five were gross errors, it found the correct solution on the second triple of points and admitted none of the errors.
Why it matters
Geometry became computable on the output of detectors that make mistakes. Least squares cannot survive that by construction: one gross error drags the estimate with it. Practical stereo, image-to-image alignment and later SLAM all start here, because all of them live on wrong correspondences.
In the same experiment a least-squares heuristic that repeatedly discards the worst residual stopped at a solution based on 18 correspondences, three of which were gross errors. The paper tabulates the expected number of trials E(k) = w to the power minus n: at a fraction of good points w = 0.5 and samples of three, that is 8.0 trials. Separately it derives k = log(1 − z)/log(1 − b); for w = 0.5, samples of four and 90 percent assurance this gives k = 35.7. For the three-point camera pose problem it proves an upper bound of four solutions. The record does not claim "23 iterations for 0.95 reliability at 50 percent outliers". That figure is not in the paper; 8.0 and 35.7 above are what is printed.